no friction currents

Achieving International Excellence at The University of Western Australia

  • Main Topic: Dynamics of Ocean Currents
    • Focus on three major balance types: Geostrophic, Inertial, and Cyclostrophic.

Equations of Motion

  • Open Ocean Dynamics: Examined terms in the equation of motion for ocean currents, highlighting important forces:
    • Coriolis Force: Affects the motion of currents due to Earth's rotation.
    • Pressure Gradient Force (PGF): Drives the movement of water from high to low pressure.
    • Other forces: Friction and Advection contribute but are less significant.
  • Identified dominant terms in the equations:
    • Largest terms are Pressure Gradient and Coriolis.

Frictionless Equations

  • Basic Equation: Acceleration = Coriolis + Pressure Gradient
  • Three Force Combinations:
    • 1. Acceleration = Coriolis
    • 2. Acceleration = Pressure Gradient
    • 3. Coriolis = Pressure Gradient
  • Understanding these combinations is crucial for analyzing flow dynamics.

Inertial Balance

  • Mathematical Representation:

    • The equations of motion indicate that when there is no PGF ( (\frac{d\rho}{dt} = 0)), the balance between acceleration and Coriolis can be expressed as:
    • \frac{du}{dt} = -f v
    • \frac{dv}{dt} = f u
    • Indicates that motions are circular and dependent on Coriolis force.

  • Oscillation: Harmonic oscillator equations are detailed:

    • \frac{d^2 v}{dt^2} + f^2 v = 0
    • Solutions indicate circular relationships, with relationships like:
    • u = V \sin(ft)
    • v = V \cos(ft)
    • Where V^2 = u^2 + v^2 .

Inertial Currents

  • Characteristics: Currents at specific depths, like those in the North Pacific demonstrate observable patterns using satellite data.
  • Example: Currents generated by a storm reflect the inertia of water movement.
  • Inertial Period: Typically shorter at poles and longer at equatorial regions - cycles around every 14 hours.

Cyclostrophic Balance

  • Balance Types:
    • Centrifugal force balances the pressure gradient force under small scale flows, leading to cyclostrophic balance.
    • Example: Tornado dynamics show significant cyclostrophic effects due to pressure gradients.

Rossby Number (Ro)

  • Significance: Evaluation of the importance of the Coriolis force in different flow scenarios:
    • Small Ro (Ro ~ 0.01): Indicates significant Coriolis influence, situated in geostrophic balance.
    • Large Ro (Ro > 100): Indicates negligible Coriolis influence, characterized by cyclostrophic balance.

Geostrophic Equations

  • Conditions:
    • Assumptions made for Geostrophic equations include: steady-state, friction negligible, and external forces limited to gravity.
  • Velocity Calculation: Can estimate velocity if the pressure gradient is known since:
    • PGF = Coriolis Force .
  • Balance Dynamics: Movement follows the gradient, highlighting the relationship between pressure and velocity directionality.

Barotropic and Baroclinic Circulation

  • Definitions:
    • Barotropic: Isopycnals parallel to isobars indicating no density variation with depth.
    • Baroclinic: Isopycnals cross isobars, leading to density variation influencing flow.

Practical Application:

  • Harmonic Motion Example: Given specific pressure values and separations, velocity can be calculated:
    • Velocity = \frac{pressure\ gradient}{density \times Coriolis \times acceleration}
  • In-depth calculations involve the relationships between hydrographic variables across related geographic stations.